Certified Kinematics Solution of 2-DOF Planar Parallel Continuum Mechanisms

Kinematics position problems in planar parallel continuum mechanisms, whose elements are elastic rods undergoing nonlinear large deformations, are ruled by a system of nonlinear differential equations. Under some conditions, those rods can be modelled as Kirchhoff rods whose equations can be solved using elliptic integrals. The resolution has to be numerical, and two approaches for that goal are shown in this paper. On the one hand, a method based in residuals evaluation finds multiple solutions at good computational rates but with no formal guarantee on the solving of all solutions. On the other hand, a procedure based on Interval Analysis constitutes a certified solution at a higher computational cost that can be improved with a Newton scheme.